Question

3 sides of right angle triangle is x, x+1 and 5. Find x and area if longest side is 5.

Answer 1

Answer:

x=3 unit and area =6 sq. unit

Step-by-step explanation:

consider the triangle in figure, since we know hypotenuse is the largest side.

therefore hypotenuse =5 units.

Now the given triangle is right angled triangle, therefore applying Pythagoras theorem.

${(ab)}^{2} + (bc) {}^{2} = {(ca)}^{2} \\ (x) {}^{2} + (x + 1) {}^{2} = (5) {}^{2} \\ {x}^{2} + {x}^{2} + 2x + 1 = 25 \\ 2 {x}^{2} + 2x = 24 \\ 2{x}^{2} + 2x - 24 = 0 \\ {x}^{2} + x - 12 = 0 \\ {x}^{2} + 4x - 3x - 12 = 0 \\ x(x + 4) - 3(x + 4) = 0 \\ (x - 3)(x + 4) = 0 \\ therefore \: x = 3 \: or \: x = - 4 \\ ignoring \: negative \: value \: because \: \\ length \: cant \: be \: negative \\ therefore \: x = 3 \\ hence \\ ab = x = 3units \\ bc = x + 1 = 3 + 1 = 4 \: units \\ ca = 5 \: units$

$now \: area \: is \: = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times (ab) \times (bc) \\ = \frac{1}{2} \times 3 \times 4 \\ = 6 \: unit {}^{2}$

mark as brainliest if helped